Samsung
Allow or Block Messages in Do Not Disturb auf Samsung
Do Not Disturb mutes all notifications on your Samsung phone by default, and that includes new SMS and MMS messages. Unless you set an exception, incoming texts stay silent and only appear once you unlock the device and check your inbox.
The setting responsible for this behavior sits inside the Do Not Disturb exceptions, separate from the general notification permissions of your messaging app. Even if the app itself is allowed to notify you, Do Not Disturb overrides it unless a message exception is defined.
To change this, open Tap on Settings ➔ Tap on Notifications ➔ Tap on Do not disturb ➔ Tap on Calls, messages and conversations ➔ Tap on Messages ➔ Choose All, Contacts only, Favorite contacts only or None.
All lets every message through, which defeats the purpose of Do Not Disturb if you get frequent texts. Contacts only filters out unknown numbers but still allows anyone saved in your address book. Favorite contacts only is the tightest filter and only lets through people you have marked as favorites, useful for family emergencies. None keeps Do Not Disturb fully silent for messages, which is the default behavior.
If you only want exceptions for specific people rather than a whole contact group, managing individual conversation settings inside the messaging app itself is usually a better fix than changing this global rule.